Numerical inequalities. Comparisons of numbers.

Numerical inequalities are mathematical statements that compare the sizes of two real numbers using symbols such as $>$, $<$, $\geq$, and $\leq$. They can be manipulated using certain rules, similar to equations, but with important differences.

Important properties

• If $a > b$ and $b > c$, then $a > c$ (transitivity).

• Adding or subtracting the same number to both sides does not change the inequality: if $a > b$, then $a + c > b + c$.

• Multiplying or dividing both sides by a positive number keeps the direction of the inequality.

• Multiplying or dividing both sides by a negative number reverses the direction of the inequality.